## Problem 04 | First Shifting Property of Laplace Transform

Problem 04
Find the Laplace transform of   $f(t) = e^t \sinh 2t$.

## Problem 03 | First Shifting Property of Laplace Transform

Problem 03
Find the Laplace transform of   $f(t) = e^{-3t} \cos t$.

## Problem 02 | First Shifting Property of Laplace Transform

Problem 02
Find the Laplace transform of   $f(t) = e^{-5t} \sin 3t$.

## Problem 01 | First Shifting Property of Laplace Transform

Problem 01
Find the Laplace transform of   $f(t) = e^{2t}t^3$.

## Problem 02 | Linearity Property of Laplace Transform

Problem 02
By using the linearity property, show that

$\mathcal{L}(\cosh at) = \dfrac{s}{s^2 - a^2}$

## Problem 01 | Linearity Property of Laplace Transform

Problem 01
Find the Laplace transform of   $f(t) = 5t - 2$.